It is totally doable, but we cannot give detailed tutorials here, since this is a simple Q&A site. So I will point you to a direction, that can lead you to the solution.
When building IOT devices with Arduino (and thats exactly, what you are doing) there are 2 internet services, that are commonly used for getting information from the device to other devices (like your phone):
- IFTTT (means If This Then That)
Both have apps and can be used to push notifications, when your IOT device does a webrequest to the service. There are also libraries for Arduino available (at least for Blynk). There are many tutorials out there, so I suggest, that you search for yourself and try some of them.
For the hardware of your IOT device, I would suggest an ESP board, because they already have Wifi build in, for example the ESP32 gives you great IO capabilities.